DATA1220-55, Fall 2024
2024-11-20
Which image shows a positive relationship between the explanatory and response variables?
Which image shows a weak relationship between the explanatory and response variables?
A correlation ranges from -1 to 1
A perfect negative correlation equals -1
A perfect positive correlation equals 1
What’s the response variable?
Response Variable: Percent of people in poverty
What’s the explanatory variable?
Explanatory variable: Percent of people who graduated high school
Describe the relationship between these 2 variables.
Relationship: linear, negative, moderate to strong
Which of the following is the most likely correlation? A) 0.60 B) -0.25 C) -0.75 D) 0.35
Which of the following is the most likely correlation? C. -0.75
\[ H_0 \colon \rho=0 \]
\[ \begin{aligned} H_A &\colon \rho > 0 \\ & \rho < 0 \\ & \rho \ne 0 \\ \end{aligned} \]
The test statistic \(t\) for the population Pearson correlation \(\rho\) (Greek letter rho) is estimated using the observed correlation \(r\).
\[ t=\frac{r\sqrt{n-2}}{\sqrt{1-r^2}} \]
Use the Student’s \(t\) distribution with degrees of freedom \(\text{df}=n-2\) to find a p-value for the observed correlation \(r\) in a sample of size \(n\) under the null hypothesis \(H_0 \colon \rho=0\).
How do we find the best line to draw through variables that appear to have a linear relationship?
Residuals are the difference between the observed values and the predicted values.
Research Question: Do ice cream sales cause sunburns?
As ice cream sales increase, the number of sunburns also increases
Strong, positive, linear correlation
High temperatures affect both ice cream consumption and behaviors that lead to sunburn
When you have a confounding variable, you might find dependence between two unrelated variables that are only connected by the confounder.
DATA1220-55 Fall 2024, Class 31 | Updated: 2024-11-20 | Canvas | Campuswire